Question

solve the inequality. graph the solution on a number line and represent the solution in interval notation when possible. 12 > -7x + 27. choose the correct graph of the solution. a. the solution is all real numbers. b. there is no solution. c. there is no solution. d. the solution written in interval notation is. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the solution written in interval notation is. b. there is no solution. it is not possible to write interval notation.

Explanation:

Step1: Solve the inequality 12 > - 7x+27

Subtract 27 from both sides.
$12 - 27>-7x+27 - 27$
$- 15>-7x$

Step2: Divide both sides by - 7 and reverse the inequality sign

$\frac{-15}{-7}<\frac{-7x}{-7}$ (When dividing an inequality by a negative number, the direction of the inequality sign changes)
$x > \frac{15}{7}$

In interval - notation, the solution is $(\frac{15}{7},\infty)$. On a number - line, we have an open circle at $\frac{15}{7}$ and an arrow pointing to the right.

Answer:

The solution written in interval notation is $(\frac{15}{7},\infty)$. The correct graph is the one with an open circle at $\frac{15}{7}$ and an arrow pointing to the right. (Based on the options in the picture, you would need to identify the graph that matches this description).